Open AccessFurther Acceleration of the Simpson Method for Solving Nonlinear Equations
Author(s) -
R. Thukral
Publication year - 2018
Publication title -
journal of advances in mathematics
Language(s) - English
Resource type - Journals
ISSN - 2347-1921
DOI - 10.24297/jam.v14i2.7415
Subject(s) - mathematics , nonlinear system , type (biology) , simple (philosophy) , order (exchange) , function (biology) , acceleration , mathematical analysis , mathematical optimization , ecology , philosophy , physics , epistemology , finance , quantum mechanics , evolutionary biology , economics , biology , classical mechanics
There are two aims of this paper, firstly, we present an improvement of the classical Simpson third-order method for finding zeros a nonlinear equation and secondly, we introduce a new formula for approximating second-order derivative. The new Simpson-type method is shown to converge of the order four. Per iteration the new method requires same amount of evaluations of the function and therefore the new method has an efficiency index better than the classical Simpson method. We examine the effectiveness of the new fourth-order Simpson-type method by approximating the simple root of a given nonlinear equation. Numerical comparisons is made with classical Simpson method to show the performance of the presented method.